Topology of Renormalization group trajectories

In The renormalization group by Matthew Schwartz the is very interesting picture of RG for dimension and dimensionless couplings:

Topology of such diagrams is very different. But this pictures describe the same system.

How from these pictures to understand, that these pictures describe the same system, but for different parametrisation of couplings?

Is it possible from some topological information from RG picture extract that this is the samr picture?

Or maybe some topological information is enough to restore initial theory?

I also add another RG picture for this theory: